Economic and Game TheoryGuessing Game

If your browser supports Java, the form below
has two buttons with numbers, plus a reset
button. If it doesn't you should exit. The
computer will try to guess which of the buttons
with numbers you will push. The number is
the probability with which it thinks you
will push that button and the score received
by the computer if you do. The computer tracks
its average score (1.0 is perfect, 0.0 means
it guessed wrong all the time), and the number
of trials. If you want to start over, push
the reset button.

Obviously it is easy to force the computer
down to a score of 0.5: just flip a coin
to determine the choice of button. Or you
could just always choose the button with
the smallest number. You will discover if
you do this for a reasonable number of trials,
the computer still gets close to 0.5. In
fact, you will discover that in a reasonable
number of trials, no matter what you do you
can't force the computer much below 0.5.
This isn't terribly interesting or challenging.
The challenge is to feed the computer some
pattern recognizable to you, and still force
the computer down to around 0.5.

If you are interested in the theory that
this program is based on, click here. If you are interested in the source code,
click here.